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<div class="header">
  <div class="headertitle"><div class="title">gaussNewtonNlls.hpp</div></div>
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<div class="contents">
<a href="gauss_newton_nlls_8hpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span> </div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="preprocessor">#pragma once</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span> </div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span><span class="preprocessor">#include &lt;array&gt;</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span><span class="preprocessor">#include &lt;functional&gt;</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span><span class="preprocessor">#include &lt;type_traits&gt;</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span><span class="preprocessor">#include &lt;utility&gt;</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span> </div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span><span class="preprocessor">#include &quot;<a class="code" href="_error_8hpp.html">NumCpp/Core/Internal/Error.hpp</a>&quot;</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span><span class="preprocessor">#include &quot;<a class="code" href="_static_asserts_8hpp.html">NumCpp/Core/Internal/StaticAsserts.hpp</a>&quot;</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span><span class="preprocessor">#include &quot;<a class="code" href="_type_traits_8hpp.html">NumCpp/Core/Internal/TypeTraits.hpp</a>&quot;</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span><span class="preprocessor">#include &quot;<a class="code" href="_core_2_shape_8hpp.html">NumCpp/Core/Shape.hpp</a>&quot;</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span><span class="preprocessor">#include &quot;<a class="code" href="_types_8hpp.html">NumCpp/Core/Types.hpp</a>&quot;</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span><span class="preprocessor">#include &quot;<a class="code" href="rms_8hpp.html">NumCpp/Functions/rms.hpp</a>&quot;</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span><span class="preprocessor">#include &quot;<a class="code" href="inv_8hpp.html">NumCpp/Linalg/inv.hpp</a>&quot;</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span><span class="preprocessor">#include &quot;<a class="code" href="_nd_array_8hpp.html">NumCpp/NdArray.hpp</a>&quot;</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span> </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespacenc_1_1linalg.html">nc::linalg</a></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>{</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    <span class="comment">//============================================================================</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    <span class="comment">// Method Description:</span></div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> dtype,</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>             <span class="keyword">typename</span>... Params,</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>             std::enable_if_t&lt;std::is_arithmetic_v&lt;dtype&gt;, <span class="keywordtype">int</span>&gt;  = 0,</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>             std::enable_if_t&lt;<a class="code hl_variable" href="namespacenc.html#a0b7796ffd2609d1e093207d8546e091a">all_arithmetic_v</a>&lt;Params...&gt;, <span class="keywordtype">int</span>&gt;  = 0,</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>             std::enable_if_t&lt;<a class="code hl_variable" href="namespacenc.html#ad3769ded44b203686d0a33dd6623e142">all_same_v</a>&lt;dtype, Params...&gt;, <span class="keywordtype">int</span>&gt; = 0&gt;</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>    std::pair&lt;NdArray&lt;double&gt;, <span class="keywordtype">double</span>&gt;</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"><a class="line" href="namespacenc_1_1linalg.html#a9de81d7c677cb58615fba70679e73f66">   77</a></span>        <a class="code hl_function" href="namespacenc_1_1linalg.html#a9de81d7c677cb58615fba70679e73f66">gaussNewtonNlls</a>(<span class="keyword">const</span> <a class="code hl_typedef" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a>                                                              numIterations,</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>                        <span class="keyword">const</span> <a class="code hl_class" href="classnc_1_1_nd_array.html">NdArray&lt;dtype&gt;</a>&amp;                                                     coordinates,</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>                        <span class="keyword">const</span> <a class="code hl_class" href="classnc_1_1_nd_array.html">NdArray&lt;dtype&gt;</a>&amp;                                                     measurements,</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>                        <span class="keyword">const</span> std::function&lt;dtype(<span class="keyword">const</span> <a class="code hl_class" href="classnc_1_1_nd_array.html">NdArray&lt;dtype&gt;</a>&amp;, <span class="keyword">const</span> <a class="code hl_class" href="classnc_1_1_nd_array.html">NdArray&lt;dtype&gt;</a>&amp;)&gt;&amp; function,</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>                        <span class="keyword">const</span> std::array&lt;std::function&lt;dtype(<span class="keyword">const</span> <a class="code hl_class" href="classnc_1_1_nd_array.html">NdArray&lt;dtype&gt;</a>&amp;, <span class="keyword">const</span> <a class="code hl_class" href="classnc_1_1_nd_array.html">NdArray&lt;dtype&gt;</a>&amp;)&gt;,</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>                                         <span class="keyword">sizeof</span>...(Params)&gt;&amp;                                      derivatives,</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>                        Params... initialGuess)</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    {</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>        <a class="code hl_define" href="_static_asserts_8hpp.html#a36abb32368b91aed0d3133a4cfd5ae92">STATIC_ASSERT_ARITHMETIC</a>(dtype);</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span> </div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>        <span class="keyword">const</span> <span class="keyword">auto</span> coordinatesShape = coordinates.<a class="code hl_function" href="classnc_1_1_nd_array.html#a4824e91b22bb46ebc31c9c08de55ef13">shape</a>();</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span> </div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        <span class="keywordflow">if</span> (coordinatesShape.rows != measurements.<a class="code hl_function" href="classnc_1_1_nd_array.html#a055875abbe80163ca91328c0fa8ffbfa">size</a>())</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>        {</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>            <a class="code hl_define" href="_error_8hpp.html#af2aff1172060367b9c5398fa097fa8fd">THROW_INVALID_ARGUMENT_ERROR</a>(<span class="stringliteral">&quot;coordinates number of rows, and measurements size must be the same.&quot;</span>);</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>        }</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span> </div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>        <a class="code hl_class" href="classnc_1_1_nd_array.html">NdArray&lt;double&gt;</a> <a class="code hl_function" href="namespacenc_1_1random_1_1detail.html#a0c948fa9b84156bdbf0e0b7b0990ceb9">beta</a> = <a class="code hl_class" href="classnc_1_1_nd_array.html">NdArray&lt;dtype&gt;</a>({ initialGuess... }).<span class="keyword">template</span> astype&lt;double&gt;().<a class="code hl_function" href="classnc_1_1_nd_array.html#a29c62da7ad489f4fc0bc706800820807">transpose</a>();</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>        <a class="code hl_class" href="classnc_1_1_nd_array.html">NdArray&lt;double&gt;</a> residuals(coordinatesShape.rows, 1);</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>        <a class="code hl_class" href="classnc_1_1_nd_array.html">NdArray&lt;double&gt;</a> jacobian(coordinatesShape.rows, <span class="keyword">sizeof</span>...(Params));</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span> </div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>        <span class="keyword">const</span> <span class="keyword">auto</span> colSlice = coordinates.<a class="code hl_function" href="classnc_1_1_nd_array.html#af03b916770d04f63d82f46110d294cd8">cSlice</a>();</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>        <span class="keywordflow">for</span> (<a class="code hl_typedef" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> iteration = 1; iteration &lt;= numIterations; ++iteration)</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>        {</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>            <span class="keywordflow">for</span> (<a class="code hl_typedef" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> measIdx = 0; measIdx &lt; coordinatesShape.rows; ++measIdx)</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>            {</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>                <span class="keyword">const</span> <span class="keyword">auto</span> coordinate = coordinates(measIdx, colSlice);</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span> </div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>                residuals[measIdx] =</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>                    <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(measurements[measIdx]) - <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(function(coordinate, <a class="code hl_function" href="namespacenc_1_1random_1_1detail.html#a0c948fa9b84156bdbf0e0b7b0990ceb9">beta</a>));</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span> </div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>                <span class="keywordflow">for</span> (<a class="code hl_typedef" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> paramIdx = 0; paramIdx &lt; <span class="keyword">sizeof</span>...(Params); ++paramIdx)</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>                {</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>                    <span class="keyword">const</span> <span class="keyword">auto</span>&amp; derivative      = derivatives[paramIdx];</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>                    jacobian(measIdx, paramIdx) = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(derivative(coordinate, <a class="code hl_function" href="namespacenc_1_1random_1_1detail.html#a0c948fa9b84156bdbf0e0b7b0990ceb9">beta</a>));</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>                }</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>            }</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span> </div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>            <span class="comment">// perform the gauss-newton linear algebra</span></div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>            <span class="keyword">const</span> <span class="keyword">auto</span> jacobianT             = jacobian.<a class="code hl_function" href="classnc_1_1_nd_array.html#a29c62da7ad489f4fc0bc706800820807">transpose</a>();</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>            <span class="keyword">const</span> <span class="keyword">auto</span> jacobianPsuedoInverse = <a class="code hl_function" href="namespacenc_1_1linalg.html#a2eeb58d0a34e50e79fcfe59f71c61b4d">linalg::inv</a>(jacobianT.dot(jacobian));</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>            <span class="keyword">const</span> <span class="keyword">auto</span> intermediate          = jacobianPsuedoInverse.dot(jacobianT);</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>            <span class="keyword">const</span> <span class="keyword">auto</span> deltaBeta             = intermediate.dot(residuals);</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>            <a class="code hl_function" href="namespacenc_1_1random_1_1detail.html#a0c948fa9b84156bdbf0e0b7b0990ceb9">beta</a> += deltaBeta;</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>        }</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span> </div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>        <span class="comment">// calculate the final rms of the residuals</span></div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>        <span class="keywordflow">for</span> (<a class="code hl_typedef" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a> measIdx = 0; measIdx &lt; coordinatesShape.rows; ++measIdx)</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>        {</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>            <span class="keyword">const</span> <span class="keyword">auto</span> coordinate = coordinates(measIdx, colSlice);</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span> </div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>            residuals[measIdx] =</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>                <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(measurements[measIdx]) - <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(function(coordinate, <a class="code hl_function" href="namespacenc_1_1random_1_1detail.html#a0c948fa9b84156bdbf0e0b7b0990ceb9">beta</a>));</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>        }</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span> </div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>        <span class="keywordflow">return</span> std::make_pair(<a class="code hl_function" href="namespacenc_1_1random_1_1detail.html#a0c948fa9b84156bdbf0e0b7b0990ceb9">beta</a>.flatten(), <a class="code hl_function" href="namespacenc.html#adc5caccd6d4c255fe829e3ef29b74c06">rms</a>(residuals).item());</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>    }</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>} <span class="comment">// namespace nc::linalg</span></div>
<div class="ttc" id="a_core_2_shape_8hpp_html"><div class="ttname"><a href="_core_2_shape_8hpp.html">Shape.hpp</a></div></div>
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<div class="ttc" id="a_error_8hpp_html_af2aff1172060367b9c5398fa097fa8fd"><div class="ttname"><a href="_error_8hpp.html#af2aff1172060367b9c5398fa097fa8fd">THROW_INVALID_ARGUMENT_ERROR</a></div><div class="ttdeci">#define THROW_INVALID_ARGUMENT_ERROR(msg)</div><div class="ttdef"><b>Definition:</b> Error.hpp:37</div></div>
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<div class="ttc" id="aclassnc_1_1_nd_array_html"><div class="ttname"><a href="classnc_1_1_nd_array.html">nc::NdArray</a></div><div class="ttdoc">Holds 1D and 2D arrays, the main work horse of the NumCpp library.</div><div class="ttdef"><b>Definition:</b> NdArrayCore.hpp:139</div></div>
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<div class="ttc" id="anamespacenc_1_1linalg_html"><div class="ttname"><a href="namespacenc_1_1linalg.html">nc::linalg</a></div><div class="ttdef"><b>Definition:</b> cholesky.hpp:41</div></div>
<div class="ttc" id="anamespacenc_1_1linalg_html_a2eeb58d0a34e50e79fcfe59f71c61b4d"><div class="ttname"><a href="namespacenc_1_1linalg.html#a2eeb58d0a34e50e79fcfe59f71c61b4d">nc::linalg::inv</a></div><div class="ttdeci">NdArray&lt; double &gt; inv(const NdArray&lt; dtype &gt; &amp;inArray)</div><div class="ttdef"><b>Definition:</b> inv.hpp:54</div></div>
<div class="ttc" id="anamespacenc_1_1linalg_html_a9de81d7c677cb58615fba70679e73f66"><div class="ttname"><a href="namespacenc_1_1linalg.html#a9de81d7c677cb58615fba70679e73f66">nc::linalg::gaussNewtonNlls</a></div><div class="ttdeci">std::pair&lt; NdArray&lt; double &gt;, double &gt; gaussNewtonNlls(const uint32 numIterations, const NdArray&lt; dtype &gt; &amp;coordinates, const NdArray&lt; dtype &gt; &amp;measurements, const std::function&lt; dtype(const NdArray&lt; dtype &gt; &amp;, const NdArray&lt; dtype &gt; &amp;)&gt; &amp;function, const std::array&lt; std::function&lt; dtype(const NdArray&lt; dtype &gt; &amp;, const NdArray&lt; dtype &gt; &amp;)&gt;, sizeof...(Params)&gt; &amp;derivatives, Params... initialGuess)</div><div class="ttdef"><b>Definition:</b> gaussNewtonNlls.hpp:77</div></div>
<div class="ttc" id="anamespacenc_1_1random_1_1detail_html_a0c948fa9b84156bdbf0e0b7b0990ceb9"><div class="ttname"><a href="namespacenc_1_1random_1_1detail.html#a0c948fa9b84156bdbf0e0b7b0990ceb9">nc::random::detail::beta</a></div><div class="ttdeci">dtype beta(GeneratorType &amp;generator, dtype inAlpha, dtype inBeta)</div><div class="ttdef"><b>Definition:</b> Random/beta.hpp:61</div></div>
<div class="ttc" id="anamespacenc_html_a0b7796ffd2609d1e093207d8546e091a"><div class="ttname"><a href="namespacenc.html#a0b7796ffd2609d1e093207d8546e091a">nc::all_arithmetic_v</a></div><div class="ttdeci">constexpr bool all_arithmetic_v</div><div class="ttdef"><b>Definition:</b> TypeTraits.hpp:67</div></div>
<div class="ttc" id="anamespacenc_html_ad3769ded44b203686d0a33dd6623e142"><div class="ttname"><a href="namespacenc.html#ad3769ded44b203686d0a33dd6623e142">nc::all_same_v</a></div><div class="ttdeci">constexpr bool all_same_v</div><div class="ttdef"><b>Definition:</b> TypeTraits.hpp:101</div></div>
<div class="ttc" id="anamespacenc_html_adc5caccd6d4c255fe829e3ef29b74c06"><div class="ttname"><a href="namespacenc.html#adc5caccd6d4c255fe829e3ef29b74c06">nc::rms</a></div><div class="ttdeci">NdArray&lt; double &gt; rms(const NdArray&lt; dtype &gt; &amp;inArray, Axis inAxis=Axis::NONE)</div><div class="ttdef"><b>Definition:</b> rms.hpp:51</div></div>
<div class="ttc" id="anamespacenc_html_af0f49663fb63332596e2e6327009d581"><div class="ttname"><a href="namespacenc.html#af0f49663fb63332596e2e6327009d581">nc::uint32</a></div><div class="ttdeci">std::uint32_t uint32</div><div class="ttdef"><b>Definition:</b> Types.hpp:40</div></div>
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